Drive units and pumps of the type mentioned here are already known. The drive units serve to drive so-called submersible oil pumps that are employed to convey oil, for instance, transmission oil. In this context, the pump, together with the preferably integrated drive unit, is completely or partially submerged in a reservoir containing the oil that is to be pumped. Prior-art drive units have a housing that surrounds a motor compartment. A rotor is arranged in this compartment. The rotor ultimately serves as the rotary drive of the pump unit in that it is joined to it by a drive shaft. A first fluid path leading from a submerged oil environment of the housing to the motor compartment is provided so as to cool the drive unit that heats up during the pumping operation. Since the pump is completely or partially submerged in the oil that it has to convey, the environment of the housing contains oil that can get into the motor compartment via the first fluid path, thereby cooling the drive unit. A drawback of prior-art drive units is that, especially during standstill phases, they fill up with oil via the first fluid path, so that a considerable portion or even the entire motor compartment is flooded with oil. When the pump is started up again as well as during operation, so-called splash losses occur since the rotor has to rotate in the oil that is present in the motor compartment, a process in which a drag torque acts upon it.